About a improper integral

I would like to ask about this integral:
integral from 2 to infinity [ ln x /(exp(x) +1) ]

I think it diverges, but I don't know how to show it diveges.

first, I thought [ ln x /(exp(x) +1) ]can't be integrate,
so I considered if it can be proved by comparing it with simpler integral.
I had try to find a smaller integral and then prove it diveges,
hence it could conclude that integral from 2 to infinity [ ln x /(exp(x) +1) ] also diveeges.
However, I could't think out such these smaller integral.

Re: About a improper integral

Originally Posted by wong999

I would like to ask about this integral:
integral from 2 to infinity [ ln x /(exp(x) +1) ]

I think it diverges, but I don't know how to show it diveges.

first, I thought [ ln x /(exp(x) +1) ]can't be integrate,
so I considered if it can be proved by comparing it with simpler integral.
I had try to find a smaller integral and then prove it diveges,
hence it could conclude that integral from 2 to infinity [ ln x /(exp(x) +1) ] also diveeges.
However, I could't think out such these smaller integral.